Abstract

We demonstrate experimentally, and describe theoretically, generation of a wide, fundamentally phase-locked Kerr frequency comb in a nonlinear resonator with a normal group velocity dispersion (GVD). A magnesium fluoride whispering-gallery mode resonator characterized with 10 GHz free spectral range and pumped either at 780 or 795 nm is used in the experiment. The envelope of the observed frequency comb differs significantly from the Kerr frequency comb spectra reported previously. We show via numerical simulation that, while the frequency comb does not correspond to generation of short optical pulses, the relative phase of the generated harmonics are fixed.

© 2014 Optical Society of America

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  1. P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
    [CrossRef]
  2. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
    [CrossRef]
  3. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, Opt. Express 21, 1335 (2013).
    [CrossRef]
  4. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
    [CrossRef]
  5. M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
    [CrossRef]
  6. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Lett. 17, 745 (1992).
    [CrossRef]
  7. S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
    [CrossRef]
  8. D. K. Serkland and P. Kumar, Opt. Lett. 24, 92 (1999).
    [CrossRef]
  9. S. Coen and M. Haelterman, Opt. Lett. 26, 39 (2001).
    [CrossRef]
  10. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
    [CrossRef]
  11. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
    [CrossRef]
  12. I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
    [CrossRef]
  13. P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
    [CrossRef]
  14. T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
    [CrossRef]
  15. C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).
  16. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  17. A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
    [CrossRef]
  18. A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
    [CrossRef]
  19. A. B. Matsko and L. Maleki, Opt. Express 21, 28862 (2013).
    [CrossRef]
  20. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 20, 27290 (2012).
    [CrossRef]
  21. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Nat. Photonics 5, 293 (2011).
    [CrossRef]
  22. A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 38, 2636 (2013).
    [CrossRef]
  23. W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 35, 2822 (2010).
    [CrossRef]
  24. D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
    [CrossRef]

2014

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

2013

2012

2011

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Nat. Photonics 5, 293 (2011).
[CrossRef]

2010

2009

2008

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

2007

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

2005

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
[CrossRef]

2001

1999

1997

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

1992

1989

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

1977

D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
[CrossRef]

Agha, I. H.

I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Arcizet, O.

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).

Beha, K.

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Byrd, J.

Chembo, Y. K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).

Coen, S.

S. Coen and M. Haelterman, Opt. Lett. 26, 39 (2001).
[CrossRef]

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

Coillet, A.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).

DelHaye, P.

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

Del-Haye, P.

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Diddams, S. A.

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

Dudley, J. M.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Eliyahu, D.

Foster, M. A.

Gaeta, A. L.

Glass, A. J.

D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
[CrossRef]

Godey, C.

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Haelterman, M.

Hansson, T.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Haus, H. A.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Henriet, R.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Holzwarth, R.

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 38, 2636 (2013).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 20, 27290 (2012).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Nat. Photonics 5, 293 (2011).
[CrossRef]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 35, 2822 (2010).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Johnson, A. R.

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Kippenberg, T. J.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Kumar, P.

Lamont, M. R. E.

Larger, L.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Levy, J. S.

Liang, W.

Lipson, M.

Maleki, L.

Matsko, A. B.

Menyuk, C. R.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Milam, D.

D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
[CrossRef]

Modotto, D.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Okawachi, Y.

Papp, S. B.

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

Saha, K.

Saleh, K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Salem, R.

Savchenkov, A. A.

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 38, 2636 (2013).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 20, 27290 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Nat. Photonics 5, 293 (2011).
[CrossRef]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Opt. Lett. 35, 2822 (2010).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Schliesser, A.

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Seidel, D.

Serkland, D. K.

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Shim, B.

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Trillo, S.

Wabnitz, S.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Lett. 17, 745 (1992).
[CrossRef]

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Weber, M. J.

D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
[CrossRef]

Wilken, T.

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Yu, N.

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

Appl. Phys. Lett.

D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977).
[CrossRef]

IEEE J. Quantum Electron.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

IEEE Photon. J.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Nat. Photonics

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Nat. Photonics 5, 293 (2011).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Nature

P. Del-Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Phys. Rev. Lett.

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

P. DelHaye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

Other

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,”arXiv:1308.2539 (2013).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experiment. Either a 780 or a 795 nm DFB semiconductor laser is self-injection locked to a magnesium fluoride WGM resonator. An optical frequency comb is generated in the resonator and analyzed using an optical spectrum analyzer. The resonator is characterized with essentially normal GVD, and the shape of comb envelope has three distinct maxima.

Fig. 2.
Fig. 2.

(a) A fundamental optical frequency comb generated with the normal GVD MgF2 WGM resonator. (b) RF signal generated at the photodiode by the comb [20 kHz resolution bandwidth (RBW)]. The comb lines separated by 10 GHz are not resolved by the optical spectrum analyzer. The red line is the Lorentzian fit of the skirts of the RF signal. Such a fit is a good measure of the instantaneous linewidth of the RF radiation.

Fig. 3.
Fig. 3.

Optical spectra of Kerr frequency combs observed at 795 nm. (a) A nearly ideal comb envelope with slightly pronounced dominance of fourth-order harmonics (seen at 40 GHz from the pump frequency). (b) The comb with dominating third-order harmonics. Both comb envelopes show some irregularities resulting from mode interaction in the multimode resonator. To switch between the regimes, we changed power and frequency of the pump light.

Fig. 4.
Fig. 4.

Numerically simulated spectra of optical frequency combs for two different pump power levels and GVD parameters: (a) D=0.039 and (b) D=0.078.

Fig. 5.
Fig. 5.

Numerically simulated envelope of intracavity optical pulses in terms of normalized amplitude |A|(g/γ)1/2 (j=1101, blue line) and the pulse formed by only a limited number of modes with no pump frequency included (j=4047, red line).

Equations (1)

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a^˙j=(2πγ+iωj)a^j+i[V^,a^j]+F0eiωtδj0,j,

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